Three-month-old Clemency was snug in a cosy white blanket and a pretty white cap with pink roses.

Kate was clearly pleased with how the morning had gone, and tweeted after her Lorraine appearance: 'Lovely tweets! – more nervous to know clemency was happy – she was… Mummy at sixes and sevens but lovely morning & lovely @reallorraine'

Looking sharp: Kate was bright and cheerful despite her early start

She replied to a tweet from the show's fitness expert Jane Wake complimenting her on how gorgeous she looked, writing: 'thanks jane! I might need some help shifting the extra two and a half stone though ;-)'

It seems little Clemency was well behaved for their early start, no doubt thanks in part to the self-confessed 'military' organisation of her mother.

Before leaving the house Kate wrote on Twitter: 'Stage one operation @reallorraine up at 6am tip toe around Clemency's crib, daddy delicately places sleeping baby in pram… Now en route'

Taking to motherhood: Kate organised their Lorraine appearance this morning like a 'military operation'

Kate spent two years undergoing IVF treatment, and after four failed attempts thought she had lost all hope of becoming a mother.

The BBC presenter, who is married to Michael Heron, a former Royal Marine, gave birth to daughter Clemency in November, describing her pregnancy as a ‘miracle’.

Shared her story: Kate went through four unsuccessful cycles of IVF before conceiving

Chubby cheeks! Clemency looked lovely in a cute pink dress

‘I still can’t quite believe that she’s here,’ she said. ‘Seeing her smile melts me to the core. It’s the culmination of everything I ever dared imagine or hope for.

‘When I have her in my arms, feeding her in the early hours, with Mike sleeping by my side, I look down at her little face and still feel overwhelmed by what’s happened.’

‘Whether it’s the beaming smile I get when I lean over her crib in the morning or when her bottom lip trembles if she’s uncertain about something, I just live for those moments now. She’s just adorable.’

Captivated her audience: Lorraine Kelly was clearly very taken with Clemency

Doting mother: Kate has described how everything Clemency does fills her with joy

Doctors warned Miss Silverton she would struggle to conceive naturally after she had to undergo surgery to remove one of her ovaries.

She then underwent four rounds of IVF, but they all failed and the couple stopped the treatment – only for Clemency to be conceived naturally soon afterwards.

Proud parents: Lorraine showed a photo of Kate and her husband Mike Heron after the birth

Miss Silverton said: ‘I’m not sure how this happened, but I will give thanks every day for the rest of my life that I have experienced giving birth and now have a daughter.

‘It’s heartbreaking to know there are so many couples out there who face the same difficulties as we did and I wish that I could spread some of our good fortune to them.’

Helping hand: Kate's husband Mike was there to lend some support during their arrival